Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation - Jia Wei; Xiaoling Han; Fumei Ye (Journal of Function Spaces)
We apply the continuation theorem of Mawhin to ensure that a fourth-order nonlinear difference equation of the form Δ4uk−2−akuαk+bkuβk=0 with periodic boundary conditions possesses at least one nontrivial positive solution, where Δuk=uk+1−uk is the forward difference operator, α>0,β>0 and α≠β, ak,bk are T-periodic functions and akbk>0. As applications, we give some examples to illustrate the application of these theorems.